The generator matrix

 1  0  1  1  1  0  1  1  1  1  1  1
 0  1 X+1 X+2  1  1  0  0  0  0  0  0
 0  0  2  0  0  0  0  0  0  2  0  0
 0  0  0  2  0  0  0  0  0  2  0  0
 0  0  0  0  2  0  0  0  0  2  0  0
 0  0  0  0  0  2  0  0  0  2  0  0
 0  0  0  0  0  0  2  0  0  2  0  0
 0  0  0  0  0  0  0  2  0  2  0  0
 0  0  0  0  0  0  0  0  2  2  0  0

generates a code of length 12 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+44x^4+32x^5+40x^6+128x^7+215x^8+192x^9+600x^10+1696x^11+2296x^12+1696x^13+600x^14+192x^15+215x^16+128x^17+40x^18+32x^19+44x^20+1x^24

The gray image is a code over GF(2) with n=48, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0458 seconds.